In on of the bigger temples in Japan supposedly has it under lock and key yeah. There's been more then a few incidents in the swords history though make it well.... Shroud of Turin case all over again

Of course you can supposedly actually go and see Durandal sticking out of a cliff.

Obviously the Dresdenverse picks and choses which particular parts of myths are true. Which is evident simply by making the identification, I think Kusanagi as Ame-no-Murakumo-no-Tsurugi is supposed to predate Imperial line and by extension Anno Domini going from when Susanoo cut it out of Orochi, and even Yamato Takeru if taken to be historical is within a century of Christ's death.